BLOW-UP ANALYSIS FOR SOME MEAN FIELD EQUATIONS INVOLVING PROBABILITY MEASURES FROM STATISTICAL HYDRODYNAMICS

摘要

Motivated by the mean fleld Sawada-Suzukiwith probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: deflned on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties of solution sequences. The optimal Trudinger-Moser inequality is also considered.